The number of planar graphs and properties of random planar graphs

Abstract

We show an asymptotic estimate for the number of labelled planar graphs on $n$ vertices. We also find limit laws for the number of edges, the number of connected components, and other parameters in random planar graphs.

Keywords

• limit law
• asymptotic enumeration
• analytic combinatorics
• normal law
• planar graph
• random graph
• [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [info.info-cg] computer science [cs]/computational geometry [cs.cg]
• [info.info-hc] computer science [cs]/human-computer interaction [cs.hc]